Table A1. Complexity of the observer’s decision rule in different models.

The left part of the table shows the number of arithmetic operations of different types for each model: linear operations (L), quadratic operations (Q), other nonlinear operations (NL), and sorting operations (Sort). The right part of the table shows the numbers of neural operations if the decision variable were directly transformed into a neural quantity using the theory of probabilistic population codes. All models have only two free parameters; only the complexity of the observer’s computation differs.

	Arithmetic Operations				Neural Operations
	Q	L	NL	Sort	a·r	b·r	Q	L	NL	Sort
Opt	32	59	8	1	164	656	724	183	20	1
Sum	0	3	0	1	4	16	15	3	1	1
Max	0	0	4	2	4	4	0	0	4	2
Min	0	0	4	2	4	4	0	0	4	2
Var	28	40	0	2	48	144	164	44	4	2
Sign	0	0	0	4	48	172	188	52	4	2
MaxT2	28	40	0	2	112	412	456	124	4	2
MaxT12	32	48	0	2	104	396	440	108	4	2
MaxT13	32	48	0	2	80	316	356	84	4	2
MaxT23	28	40	0	2	160	652	720	172	4	2
MaxT123	32	48	0	2	4	4	0	11	12	1
SumErf	0	7	4	1	12	16	12	19	20	1
SumErfT1	8	11	8	1	52	176	192	63	20	1
SumErfT2	28	51	8	1	52	148	168	55	20	1
SumErfT3	28	51	8	1	116	416	460	135	20	1
SumErfT12	32	59	8	1	108	400	444	119	20	1
SumErfT13	32	59	8	1	84	328	360	95	20	1
SumErfT23	28	51	8	1	12	16	12	11	12	1
SumXT1	8	7	4	1	52	176	192	55	12	1
SumXT2	28	47	4	1	52	148	162	47	12	1
SumXT3	28	47	4	1	116	416	460	127	12	1
SumXT12	32	55	4	1	108	400	444	111	12	1
SumXT13	32	55	4	1	84	320	360	87	12	1
SumXT23	28	47	4	1	164	656	724	175	12	1
SumXT123	32	55	4	1	164	656	724	183	20	1